65ed4
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Prime factorization
5 × 13
Step size
36.9231¢
Octave
33\65ed4 (1218.46¢)
Twelfth
52\65ed4 (1920¢) (→4\5ed4)
Consistency limit
1
Distinct consistency limit
1
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← 63ed4 | 65ed4 | 67ed4 → |
65 equal divisions of the 4th harmonic (abbreviated 65ed4) is a nonoctave tuning system that divides the interval of 4/1 into 65 equal parts of about 36.9 ¢ each. Each step represents a frequency ratio of 41/65, or the 65th root of 4.
Intervals
Steps | Cents | Approximate ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 36.9 | |
2 | 73.8 | 23/22 |
3 | 110.8 | 33/31 |
4 | 147.7 | |
5 | 184.6 | |
6 | 221.5 | 33/29 |
7 | 258.5 | |
8 | 295.4 | |
9 | 332.3 | 17/14, 23/19 |
10 | 369.2 | 21/17, 26/21 |
11 | 406.2 | 19/15 |
12 | 443.1 | 22/17 |
13 | 480 | 29/22 |
14 | 516.9 | 31/23 |
15 | 553.8 | |
16 | 590.8 | 31/22 |
17 | 627.7 | 33/23 |
18 | 664.6 | 22/15 |
19 | 701.5 | 3/2 |
20 | 738.5 | 23/15, 26/17 |
21 | 775.4 | |
22 | 812.3 | |
23 | 849.2 | 31/19 |
24 | 886.2 | |
25 | 923.1 | 29/17 |
26 | 960 | |
27 | 996.9 | |
28 | 1033.8 | |
29 | 1070.8 | 13/7 |
30 | 1107.7 | 19/10 |
31 | 1144.6 | 29/15, 33/17 |
32 | 1181.5 | |
33 | 1218.5 | |
34 | 1255.4 | 31/15 |
35 | 1292.3 | |
36 | 1329.2 | |
37 | 1366.2 | 11/5 |
38 | 1403.1 | 9/4 |
39 | 1440 | 23/10 |
40 | 1476.9 | |
41 | 1513.8 | |
42 | 1550.8 | |
43 | 1587.7 | |
44 | 1624.6 | |
45 | 1661.5 | |
46 | 1698.5 | |
47 | 1735.4 | |
48 | 1772.3 | |
49 | 1809.2 | |
50 | 1846.2 | 29/10 |
51 | 1883.1 | |
52 | 1920 | |
53 | 1956.9 | 31/10 |
54 | 1993.8 | |
55 | 2030.8 | |
56 | 2067.7 | 33/10 |
57 | 2104.6 | 27/8 |
58 | 2141.5 | |
59 | 2178.5 | |
60 | 2215.4 | |
61 | 2252.3 | |
62 | 2289.2 | |
63 | 2326.2 | |
64 | 2363.1 | |
65 | 2400 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +18.5 | +18.0 | +0.0 | -17.1 | -0.4 | -8.8 | +18.5 | -0.8 | +1.4 | -15.9 | +18.0 |
Relative (%) | +50.0 | +48.9 | +0.0 | -46.3 | -1.1 | -23.9 | +50.0 | -2.3 | +3.7 | -43.2 | +48.9 | |
Steps (reduced) |
33 (33) |
52 (52) |
65 (0) |
75 (10) |
84 (19) |
91 (26) |
98 (33) |
103 (38) |
108 (43) |
112 (47) |
117 (52) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -9.8 | +9.6 | +1.0 | +0.0 | +5.8 | +17.6 | -2.1 | -17.1 | +9.2 | +2.5 | -0.6 |
Relative (%) | -26.4 | +26.1 | +2.6 | +0.0 | +15.7 | +47.7 | -5.8 | -46.3 | +25.0 | +6.8 | -1.6 | |
Steps (reduced) |
120 (55) |
124 (59) |
127 (62) |
130 (0) |
133 (3) |
136 (6) |
138 (8) |
140 (10) |
143 (13) |
145 (15) |
147 (17) |